Properties

Label 1342.2.a
Level 1342
Weight 2
Character orbit a
Rep. character \(\chi_{1342}(1,\cdot)\)
Character field \(\Q\)
Dimension 49
Newforms 14
Sturm bound 372
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1342 = 2 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1342.a (trivial)
Character field: \(\Q\)
Newforms: \( 14 \)
Sturm bound: \(372\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1342))\).

Total New Old
Modular forms 190 49 141
Cusp forms 183 49 134
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(11\)\(61\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(8\)
Plus space\(+\)\(20\)
Minus space\(-\)\(29\)

Trace form

\(49q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 49q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 41q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(49q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 49q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 41q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 49q^{16} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut -\mathstrut 13q^{18} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 47q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 10q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 10q^{34} \) \(\mathstrut +\mathstrut 32q^{35} \) \(\mathstrut +\mathstrut 41q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 24q^{42} \) \(\mathstrut -\mathstrut 28q^{43} \) \(\mathstrut +\mathstrut q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 16q^{46} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 17q^{49} \) \(\mathstrut -\mathstrut 31q^{50} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut -\mathstrut 14q^{52} \) \(\mathstrut -\mathstrut 14q^{53} \) \(\mathstrut +\mathstrut 8q^{54} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 8q^{56} \) \(\mathstrut -\mathstrut 32q^{57} \) \(\mathstrut -\mathstrut 22q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 49q^{64} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 36q^{67} \) \(\mathstrut +\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 80q^{69} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 13q^{72} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut -\mathstrut 14q^{74} \) \(\mathstrut +\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 12q^{76} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 32q^{79} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 25q^{81} \) \(\mathstrut -\mathstrut 10q^{82} \) \(\mathstrut +\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 8q^{84} \) \(\mathstrut -\mathstrut 36q^{85} \) \(\mathstrut -\mathstrut 20q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 56q^{91} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut +\mathstrut 24q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut -\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 46q^{97} \) \(\mathstrut +\mathstrut 7q^{98} \) \(\mathstrut +\mathstrut 13q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1342))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 11 61
1342.2.a.a \(1\) \(10.716\) \(\Q\) None \(-1\) \(1\) \(-2\) \(4\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots\)
1342.2.a.b \(1\) \(10.716\) \(\Q\) None \(1\) \(-1\) \(-4\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-2q^{7}+\cdots\)
1342.2.a.c \(1\) \(10.716\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1342.2.a.d \(1\) \(10.716\) \(\Q\) None \(1\) \(3\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+3q^{3}+q^{4}+3q^{6}+2q^{7}+q^{8}+\cdots\)
1342.2.a.e \(2\) \(10.716\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
1342.2.a.f \(2\) \(10.716\) \(\Q(\sqrt{5}) \) None \(2\) \(3\) \(2\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}+2\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
1342.2.a.g \(3\) \(10.716\) 3.3.148.1 None \(3\) \(-3\) \(-4\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1342.2.a.h \(4\) \(10.716\) 4.4.14656.1 None \(-4\) \(-2\) \(-2\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
1342.2.a.i \(4\) \(10.716\) 4.4.48396.1 None \(-4\) \(-2\) \(0\) \(3\) \(+\) \(+\) \(-\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
1342.2.a.j \(4\) \(10.716\) 4.4.2225.1 None \(4\) \(-2\) \(4\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots\)
1342.2.a.k \(5\) \(10.716\) 5.5.3362852.1 None \(-5\) \(-2\) \(0\) \(-3\) \(+\) \(+\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
1342.2.a.l \(6\) \(10.716\) 6.6.8248384.1 None \(6\) \(-3\) \(-4\) \(-9\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(\beta _{3}-\beta _{5})q^{5}+\cdots\)
1342.2.a.m \(6\) \(10.716\) 6.6.136632976.1 None \(6\) \(2\) \(2\) \(5\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
1342.2.a.n \(9\) \(10.716\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(5\) \(6\) \(-2\) \(+\) \(-\) \(+\) \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1342))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1342)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(122))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(671))\)\(^{\oplus 2}\)